P2480 [SDOI2010]古代猪文

gdnCnn/dmod999911659g^{\sum_{d|n}C_{n}^{n/d}} \mod 999911659

gdnCndmod999911659g^{\sum_{d|n}C_{n}^{d}} \mod 999911659

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P3312 [SDOI2014]数表

i=1nj=1mσ((i,j))\sum_{i=1}^n\sum_{j=1}^m \sigma((i,j))

d=1min(n,m)σ(d)i=1nj=1m[gcd(i,j)=d]\sum_{d=1}^{\min(n,m)}\sigma(d)\sum_{i=1}^n\sum_{j=1}^m [gcd(i,j)=d]

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P6055 [RC-02] GCD

这道题的反推还是挺有意思的。

i=1nj=1np=1njq=1nj[(i,j)=1][(p,q)=1]\sum_{i=1}^n\sum_{j=1}^n\sum_{p=1}^{\lfloor \frac{n}{j} \rfloor}\sum_{q=1}^{\lfloor \frac{n}{j} \rfloor}[(i,j)=1][(p,q)=1]

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SP26108 TRENDGCD - Trending GCD

i=1nj=1mij(i,j)μ2((i,j))\sum_{i=1}^n\sum_{j=1}^m ij (i,j)\mu^2((i,j))

k=1min(n,m)i=1nj=1m[(i,j)=k]ijkμ2(k)\sum_{k=1}^{\min(n,m)}\sum_{i=1}^n\sum_{j=1}^m [(i,j)=k]ij k\mu^2(k)

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